Magnetoconductance signatures of chiral domain-wall bound states in magnetic topological insulators

Recent magnetoconductance measurements performed on magnetic topological insulator candidates have revealed butterfly-shaped hysteresis. This hysteresis has been attributed to the formation of gapless chiral domain-wall bound states during a magnetic-field sweep. We treat this phenomenon theoretically, providing a link between microscopic magnetization dynamics and butterfly hysteresis in magnetoconductance. Further, we illustrate how a spatially resolved conductance measurement can probe the most striking feature of the domain-wall bound states: their chirality. This work establishes a regime where a definitive link between butterfly hysteresis in longitudinal magneto-conductance and domain-wall bound states can be made. This analysis provides an important tool for the identification of magnetic topological insulators.

Figure 1

(a) Source and drain electrodes laid on the surface of a three-dimensional topological insulator having a ferromagnetic surface. (b) The magnetic subsystem is modeled as a one-dimensional Ising chain with periodic boundary conditions. Domain walls support chiral domain-wall bound states (DWBSs). (c) The DWBSs form at a domain wall, where the Dirac mass changes sign as the magnetization reverses.

Figure 2

(a) Simulated conductance (blue) and magnetization (red) during a single field sweep. At $b=b_i>\xi$, a counterpolarized domain nucleates and grows across the sample. At $b=b_f$, the domain has consumed the sample. While the domain is growing, the conductance jumps to $G_0=e^2/h$. The typical width of a conductance plateau is $\mathrm{\Delta }b$. (b) The trial-averaged conductance is peaked at $b=\xi +\mathrm{\Delta }{b}_{+}$ ($\mathrm{\Delta }{b}_{+}\propto \sqrt{v}$), with maximum value $G^{*}=G_0(\mathrm{\Delta }b/\mathrm{\Delta }{b}_{+})exp\left(-1/2\right)\propto \sqrt{v}$, where $v=db/dt$ is the sweep rate.

Figure 3

(a) Segmented gates can be used in the Corbino geometry to spatially resolve bias-dependent conductance from DWBSs to establish their chirality. (b) Probability density for the outward-conducting (blue) and inward-conducting (green) DWBSs nucleating at $x=0$ and diffusing via a directed random walk before annihilating at $\left|x\right|\simeq N/2$ for $N\gg 1$ spins. To produce this plot, we have taken $N=50\gg 1$ spins, leading to well-resolved trajectories.